To remove the Blogger Navbar, open any of the Design/Template/Layout tabs, depending on the kind of template used on the blog. Then click on "Edit HTML" in order to edit the blog template's HTML code.
Add the following CSS right below the Blog credits comment:
#navbar-iframe { display: none !important; }
#b-navbar { height: 0px; visibility: hidden; }
body { position: relative; top: -32px; }
The Blog Credits comment (sample) looks like this:
/*-----------------------------------------------
Blogger Template Style
Name: Picture Window
Designer: Josh Peterson
URL: www.noaesthetic.com
----------------------------------------------- */
Save the changes to the template by clicking the "Save Template" button.
Now view your blog page, the NavBar is gone!
